Syllabus: The existence of Riemann integral for sufficiently well behaved functions. Fundamental
theorem of Calculus, computation of definite integrals, improper integrals,
sequences and series of functions, double sequences, pointwise versus uniform convergence
for a function defined on an interval of R, term by term differentiation and
integration, the Weierstrasss theorem about uniform approximation of a continuous
function by a sequence of polynomials on a closed bounded interval. Radius of convergence
of power series and real analyticity of functions.
Reference Texts:
(a) T. M. Apostol: Mathematical Analysis.
(b) T. M. Apostol: Calculus.
(c) S. Dineen: Multivariate Calculus and Geometry.
(d) R. R. Goldberg: Methods of Real Analysis.
(e) T. Tao: Analysis I & II.
(f) Bartle and Sherbert: Introduction to Real Analysis.
(g) H. Royden: Real Analysis.
K. A. Ross: Elementary Analysis.
https://www.isibang.ac.in/~adean/infsys/database/Bmath/RA2.html
- Teacher: Jaydeb Sarkar